Calculus II/Vector Geometry Operation

Addition and Subtraction

 * [[image:VectorOperations.png|400px]]

If $$\mathbf{a}\,$$ and $$\mathbf{b}\,$$ are vectors,

Then the sum
 * $$\mathbf{c} = \mathbf{a} + \mathbf{b}\,$$ is also a vector (see Figure 2(a)).

The two vectors can also be subtracted from one another to give another vector
 * $$\mathbf{d} = \mathbf{a} - \mathbf{b}\,$$.

Multiplication by a scalar
Multiplication of a vector $$\mathbf{b}\,$$ by a scalar $$\lambda\,$$ has the effect of stretching or shrinking the vector (see Figure 2(b)).

You can form a unit vector $${\mathbf{\hat b}}\,$$ that is parallel to $$\mathbf{b}\,$$ by dividing by the length of the vector $$|\mathbf{b}|\,$$. Thus,

{\mathbf{\hat b}} = \cfrac{\mathbf{b}}{|\mathbf{b}|} ~. $$